CBSE 2025, Set 1

Question

(a) Draw the energy-band diagrams for conductors, semiconductors and insulators at $T = 0$ K. How is an electron-hole pair formed in a semiconductor at room temperature ?

(b) Carbon and silicon both are members of Group IV of the periodic table and have the same lattice structure. Carbon is an insulator whereas silicon is a semiconductor. Explain.

Edvaya · Accepted Answer

The correct answer is Subjective. **(a) Energy-band diagrams at T = 0 K:** ![Energy band diagrams for conductors, semiconductors and insulators](https://www.edvaya.com/images/cbse/physics/2025/set1/q22-energy-band-diagrams.webp) **Conductors:** The conduction band and valence band overlap (or the conduction band is partially filled), so electrons are freely available for conduction even at 0 K. **Semiconductors:** There is a small energy gap ($E_g 3$ eV, e.g., diamond: 5.5 eV). Electrons cannot cross this gap under normal conditions. **Electron-hole pair formation in semiconductor at room temperature:** At room temperature, thermal energy (~$k_BT \approx 0.026$ eV at 300 K) is sufficient to excite some electrons from the valence band to the conduction band. When an electron is excited, it leaves behind a vacant site in the valence band, called a **hole** (positive charge carrier). This process creates an **electron-hole pair**. The excited electron in the conduction band is free to conduct electricity, and the hole in the valence band also acts as a positive charge carrier. *(½ mark)* **(b) Carbon vs Silicon — why one is insulator, other is semiconductor:** Both C and Si are in Group IV, with 4 valence electrons, and both form covalent diamond-cubic lattice structures. The key difference is the **band gap**: | Property | Carbon (Diamond) | Silicon | |---|---|---| | Band gap $E_g$ | ~5.5 eV (very large) | ~1.1 eV (small) | | Classification | Insulator | Semiconductor | In carbon (diamond), the valence electrons are held very tightly due to the **smaller atomic size** (C is the second period element). The covalent bonds are much stronger, the bond length is shorter, and the energy required to break a bond and promote an electron to the conduction band is very large (~5.5 eV). This large band gap makes diamond an insulator. In silicon, the atomic radius is larger (third period element), covalent bonds are weaker, and the band gap is only ~1.1 eV. At room temperature, thermal energy can promote electrons across this gap, making silicon a semiconductor. > **Key point:** Same structure, different band gap — the difference arises from atomic size and bond strength.

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